To graph the compound inequality [tex]\( x \geq 8 \text{ or } x < -7 \)[/tex] on a number line, follow these steps:
1. Graph [tex]\( x \geq 8 \)[/tex]:
- Identify the point [tex]\( x = 8 \)[/tex] on the number line.
- Since [tex]\( x \geq 8 \)[/tex] includes the number 8, use a closed circle at 8. This indicates that 8 is part of the solution.
- Shade the region to the right of 8, extending to positive infinity (∞). This represents all numbers greater than or equal to 8.
2. Graph [tex]\( x < -7 \)[/tex]:
- Identify the point [tex]\( x = -7 \)[/tex] on the number line.
- Since [tex]\( x < -7 \)[/tex] does not include the number -7, use an open circle at -7. This indicates that -7 is not part of the solution.
- Shade the region to the left of -7, extending to negative infinity (-∞). This represents all numbers less than -7.
The final graph on the number line will have:
- A closed circle at 8 with shading extending to the right.
- An open circle at -7 with shading extending to the left.
This visualization helps in understanding the solution set for the compound inequality [tex]\( x \geq 8 \text{ or } x < -7 \)[/tex].
Here’s how it looks:
```
<-----(-∞)=====(-7)=====8=====>(∞)
o ●
```
- [tex]\[Open circle at -7 indicates it is not included.\][/tex]
- [tex]\[Closed circle at 8 indicates it is included.\][/tex]
